Answer
$x=16$
Work Step by Step
RECALL:
(i) $\log_b{x}=y \longrightarrow b^y=x.$
(ii) $a^{\frac{m}{n}}=(\sqrt[n]{a})^m.$
Use rule (i) above to write the given equation in exponential form, then solve the equation:
$\begin{array}{ccc}
&64^{\frac{2}{3}} &= &x\end{array}$
use rule (ii) above to obtain
$\begin{array}{ccc}
\\(\sqrt[3]{64})^2 &= &x
\\(\sqrt[3]{4^3})^2 &= &x
\\(4)^2 &= &x
\\16 &= &x
\end{array}.$
Thus, $x=16$.
